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Randomness and Predictability in Dynamic Chaos

  • Chapter
Nonlinear Waves

Part of the book series: Research Reports in Physics ((RESREPORTS))

Abstract

The basic representations on randomness and determinism of real physical phenomena are considered and the concept of partially deterministic processes and fields is proposed. This concept uses predictability (unpredictability) as a criterion of determinism (randomness). The coefficient of correlation between the observed and modelled (forecasted, hypothetical) processes is proposed to be used as the degree of determinability. Theoretical and numerical analyses of some systems possessing strange attractors have shown that the time of deterministic (predictable) behavior Ď„det, may noticeably exceed the coherence time.

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References

  1. A. M. Kolmogorov. Three approaches to the quantity definition of information, Problems of information transmission, 1965, v.1, 1–22 (in Russian).

    Google Scholar 

  2. A. S. Shen. Frequency approach to the definition of random sequences. In: Semiotika i informatika, M., VINITI Publ., 1982, No. 18, 14–42 (in Russian).

    Google Scholar 

  3. P. Martin-Lof. The definition of random sequences. Information Control, 1966, v.9, 602.

    Article  MathSciNet  Google Scholar 

  4. A. K. Zvonkin, L. A. Levin. Complexity of finite objects and the development of the concepts information and randomness by means of algorithm theory. Uspekhi Matematicheskykh Nauk, 1970, v.25, 85–101 (in Russian).

    MathSciNet  Google Scholar 

  5. R. Shaw. Strange attractor, chaotic behaviour and information flow. zeitschrift fur Naturforschung, 1981, v.36a, 80–102.

    ADS  Google Scholar 

  6. J. P. Crutchfield, N. H. Packard. Symbolic dynamics of one-dimensional map: entropies, finite precision and noise. Internat. J. Theor. Phys., 1982, v.21, No.5/7, 433–466.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. J. P. Crutchfield, N. H. Packard. Symbolic dynamics of noisy chaos. Physica, 1983, v.7D, No.2, 202–223.

    ADS  MathSciNet  Google Scholar 

  8. Yu. A. Kravtsov, V. S. Etkin. On the role of fluctuation forces in dynamics of autostochastic systems: the limit of predictability time and destruction of weak periodical regimes. Izvestiya Vysshykh Ucheb- nykh Zavedenii - Radiofizika, 1981, v.24, No.8, 992–998 (English translation: Radiophysics and Quantum Electronics, 1981, v.24).

    Google Scholar 

  9. Yu. A. Kravtsov, V. S. Etkin. Dynamic correlation and predictability in stochastic dynamic systems in the presence of fluctuations. In: Nonlinear and Turbulent Processes in Physics / Ed. by R. Z. Sagdeev, vol.3, Harwood Acad. Publishers, N.Y., 1984, 1411–1417.

    Google Scholar 

  10. Yu. A. Kravtsov, V. S. Etkin. Degree of dynamic correlation and revealing the dynamic nature of random processes. Radiotekhnika i Elek- tronika, 1984, v.29, No.12, 1358–2364 (in Russian).

    Google Scholar 

  11. L. Sh. Il’kova, Yu. A. Kravtsov, O. S. Mergelyan, V. S. Etkin. Measure of partial determinism of dynamic chaos. Izvestiya Vysshykh Uchebnykh Zavedenii - Radiofizika, 1985, v.28, No.7, 929–932 (English translation: Radiophysics and Quantum Electronics, 1985, v.28).

    Google Scholar 

  12. Yu. A. Kravtsov, V. G. Petnikov. Partially deterministic wavefields. Doklady Akademii Nauk USSR, 1985, v.284, No.7, 1035–1038 (English translation: Sov. Phys. - Doklady, 1985).

    Google Scholar 

  13. Yu. A. Kravtsov, V. G. Petnikov. Partially deterministic wavefields in optics. J. Opt. Soc. Amer. A. 1987, v.4, No.1, 11–15.

    Article  ADS  Google Scholar 

  14. L. Sh. Il’kova, Yu. A. Kravtsov, A. S. Pikovskii. Determination of the degree of determinism for experimentally observed chaotic regimes. Kratkie Soobsheniya FIAN po Fizike, 1986, No.11, 7–9 (English translation: Sov. Phys. Lebedev Institute Reprints, 1986).

    Google Scholar 

  15. E. B. Vul, Ya. G. Sinai, K. M. Khanin. Universality of Feigenbaum and thermodynamical formalism. Uspekhi Matematicheskykh Nauk, 1984, v.39, 1–39 (in Russian).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of General Physics, USSR Academy of Sciences, Moscow, USSR

    Yu. A. Kravtsov

Authors
  1. Yu. A. Kravtsov
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Editor information

Editors and Affiliations

  1. Institute of Applied Physics, ul. Ulyanova 46, SU-603600, Gorky, USSR

    Andrei V. Gaponov-Grekhov (Academician) & Mikhail I. Rabinovich (Academician) & 

  2. Institute of Cybernetics, Estonian SSR Academy of Sciences, Akadeemia tee 21, SU-200108, Tallinn, USSR

    JĂĽri Engelbrecht

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© 1989 Springer-Verlag Berlin Heidelberg

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Kravtsov, Y.A. (1989). Randomness and Predictability in Dynamic Chaos. In: Gaponov-Grekhov, A.V., Rabinovich, M.I., Engelbrecht, J. (eds) Nonlinear Waves. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74366-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-74366-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50654-6

  • Online ISBN: 978-3-642-74366-5

  • eBook Packages: Springer Book Archive

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